# 13.1: Inverse Variation

**At Grade**Created by: CK-12

*This activity is intended to supplement Algebra I, Chapter 12, Lesson 1.*

## Part 1 - Enter the Data

Enter the data from the table into lists.

Press **STAT ENTER**. Enter the \begin{align*}x\end{align*}

\begin{align*}x\end{align*} |
\begin{align*}y\end{align*} |
---|---|

1 |
\begin{align*} 24\end{align*} |

2 |
\begin{align*}12\end{align*} |

3 |
\begin{align*}8\end{align*} |

4 |
\begin{align*}6\end{align*} |

5 |
\begin{align*}4.8\end{align*} |

6 |
\begin{align*}4\end{align*} |

Press \begin{align*}Y=\end{align*}**Plot1**.

Press **ENTER** to turn the plot **On**. Select **scatter** as the type of plot, \begin{align*}L1\end{align*}

Press **WINDOW**. Set the window to the following:

\begin{align*}Xmin = 0,\ Xmax = 10,\ Xscl = 2\end{align*}

\begin{align*}Ymin = 0,\ Ymax = 25,\ Yscl = 5\end{align*}

Press **GRAPH**.

## Part 2 - Questions

- How would you describe the relationship between \begin{align*}x\end{align*}
x and \begin{align*}y\end{align*}y by examining this data?

Press **STAT ENTER** to return to the lists.

- What relationships can you see by examining the numbers in the lists?
- What is the product of each pair of numbers?

Arrow to the top of \begin{align*}L3\end{align*}

Press **ENTER** to execute the formula. The product in each case is \begin{align*}24\end{align*}

- What type of situation might this be a formula for?

Solve the equation \begin{align*}x \cdot y = 24\end{align*}

- What is your equation?

Press **GRAPH**.

- What other information can you find from the graph of the equation that you could not gather from the plot?
- Does this graph appear to be a function? Explain.

Press \begin{align*}2^{nd}\end{align*}**[TABLE]** to examine the function table.

- What is happening when \begin{align*}x = 0\end{align*}
x=0 ? Why?

Arrow up to the negative \begin{align*}x-\end{align*}

- What do you notice about the \begin{align*}y-\end{align*}
y− values? - Why does this occur?
- What do you think the graph of your equation looks like to the left of the \begin{align*}y-\end{align*}
y− axis?

Press **WINDOW**. Set the window as shown to examine the graph when \begin{align*}x\end{align*}

Press **GRAPH**.

- What appears to be happening when \begin{align*}x = 0\end{align*}
x=0 ? - Why does the graph of the equation not appear in Quadrants II or IV?
- Do you think an inverse variation can ever be found in Quadrants II or IV? Why?
- Does this graph appear to be a function now? Explain.

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